(x-2)(x-3)=x

Solution for (x-2)(x-3)=x equation:

(x-2)(x-3)=x

We move all terms to the left:

(x-2)(x-3)-(x)=0

We add all the numbers together, and all the variables

-1x+(x-2)(x-3)=0

We multiply parentheses ..

(+x^2-3x-2x+6)-1x=0

We get rid of parentheses

x^2-3x-2x-1x+6=0

We add all the numbers together, and all the variables

x^2-6x+6=0

a = 1; b = -6; c = +6;
Δ = b2-4ac
Δ = -62-4·1·6
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*1}=\frac{6-2\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*1}=\frac{6+2\sqrt{3}}{2}
$